Pitch Systems

Combinatorial Tetrachords

Speculating on Milton Babbit’s “all-combinatorial hexachords” based on set theory, and on the idea of the division of the chromatic range into four mutually exclusive triads, I thought I’d come up with quadriads instead, as they represent a much used vehicle in improvisation (at least as used as the aforementioned formations).

which deals with Malik’s system of tonal signatures, I thought I’d post the ones that are found in Messiaen’s sixth mode of limited transposition (tone,tone,semitone,semitone,tone,tone,semitone,semitone – in other words the first tetrachord of a major scale repeated with a tritone steer).

In C, these are:

m3Eb (F,Gb,C,D)
m3A (B,C,F#,G#)

h3Eb (F,Bb,B,D)
h3A (B,E,F,G#)

The original article deals only with nested tonal signatures in regards to Messiaen’s third and seventh mode, so I thought this would be a nice addition as I find the sixth quite useful too…